A review of Labour's policy on Trident could make its recommendations before a crunch Commons vote - potentially leading to another major shadow cabinet split.
Labour's policy is still officially in favour of maintaining the nuclear deterrent with submarines deployed around the clock able to launch a strike, but leader Jeremy Corbyn is committed to scrapping Trident.
His ally Ken Livingstone, who is co-chairing a review of Labour's defence policy, said the sections of the work relating to Trident could be completed in "eight to 10 weeks", which could mean recommending a change in the party's policy before David Cameron calls a vote giving the green light to a new generation of submarines to carry the nuclear missiles.
Mr Corbyn's contentious reshuffle saw Trident opponent Emily Thornberry appointed shadow defence secretary in place of pro-renewal Maria Eagle.
No date has yet been set for the Commons vote but the review led by Mr Livingstone, now alongside Ms Thornberry rather than Ms Eagle, will prioritise the work on Trident.
The former London mayor told BBC Two's Newsnight: "We will desperately try and do it as rapidly as possible. So we will focus on the Trident issue ahead of the rest of the defence review ... With a bit of luck that can be done in eight to 10 weeks.
"It will take a lot of work for me and Emily, but that's good."
Any attempt to change the official party policy would take longer, with the annual conference in September required to ratify a new position - something that could prove difficult if trade unions oppose scrapping Trident and the valuable defence jobs that come with it.
Shadow minister without portfolio Jon Ashworth conceded that the party's splits on Trident may lead to a repeat of the situation faced by Mr Corbyn over the decision on bombing Islamic State (IS) in Syria, where he was forced to allow a free vote.
Asked if there could be a repeat of the position where the leader and members of his shadow cabinet took opposing positions, Mr Ashworth said it was "not desirable, but I suspect it's inevitable".
He told BBC Two's Daily Politics: "We always try to get a collective position, we tried to get a collective position on Syria for example, but we weren't able to and we had a free vote. That may well be the territory we are in."
Former home secretary Alan Johnson said Labour must avoid another split, telling Newsnight: "One thing's for sure, we can't have two different positions."
He added: "I'm pro-Trident. I'm pro-nuclear disarmament through multilateral disarmament. I think everyone is looking for nuclear disarmament, it's the best way to get there."
Labour MP John Woodcock, whose Barrow and Furness seat includes the boatyards where the new submarines would be built, told Newsnight that a row over Trident was futile because the project would go ahead regardless of his party's divisions.
He said: "Let's focus on something where we actually can make a difference for the people who desperately need Labour to be a credible opposition, rather than spending time tearing ourselves apart as a party for something which is going to happen anyway - there is a cast-iron majority in Parliament for this project to go past the point of no return.
"So no matter what Jeremy does, or even if he were to magic up a changed policy - which he won't - it's not going to make a difference to the fact that these submarines are going to be renewed."
Former shadow education secretary Tristram Hunt denounced the "divisiveness and futility" of Mr Corbyn's reshuffle as the latest appointment to his top team was announced.
In the latest stage of the reshuffle, Jo Stevens was appointed shadow solicitor general.
She takes over from Karl Turner, who was promoted to shadow attorney general on Monday following the resignation of Catherine McKinnell.
Writing in The Spectator, Mr Hunt - who refused to serve on the Corbyn frontbench - said that the shake-up had distracted attention from Labour campaigns on flooding, Europe and housing.
"You will recall that Europe spokesman Pat McFadden was sacked for suggesting that terrorists should be held accountable for their crimes. Shadow defence secretary Maria Eagle was moved for supporting Labour Party policy. And culture minister Michael Dugher got the axe for not living in Islington," said Mr Hunt.
But in a sign of the revival of the party's grassroots, a survey of more than 100 constituency Labour parties by The Guardian found that almost every one reported membership numbers at least doubling since Mr Corbyn stood for the leadership - with some saying they had five times as many members as before and others reporting the revival of branches which had been near to closing for lack of support.
Overall Labour membership has increased from 201,293 at the time of the May 2015 general election to 388,407 this month, with the total of 13,860 who have left since the election vastly outnumbered by new recruits, said the newspaper.
The Guardian reported that there had been two surges of new members signing up, the first coming after Mr Corbyn joined the battle to succeed Ed Miliband and the second after he was elected leader.
A Labour spokeswoman said that membership stood at around 380,000 in December and was continuing to grow, but declined to give further details.